{
  "abstract": "We introduce sHAIL-Causal, the causal specialization of the Saturated Hierarchical Atomic Incremental Learning (sHAIL) paradigm: a sequential staircase procedure that ascends a nested hierarchy of hypothesis classes H_0 < H_1 < ... < H_K once a saturation signal indicates that mastery of the current stage has plateaued. Where general sHAIL leaves the saturation criterion open, sHAIL-Causal instantiates it with a joint criterion of goodness-of-fit saturation and cross-environment invariance, replacing the complexity control of Structural Risk Minimization. We show, theoretically and by simulation, that complexity-only staircases are seduced by confounded predictors that lower empirical risk without reflecting stable causal structure, whereas an invariance-gated staircase provably halts at the true causal predictor set under a per-variable Richness condition. We show that naive greedy search fails to recover the causal set even under Richness, trace the failure to non-monotonicity of the invariance statistic along single-variable paths, and validate a fix combining bounded-exhaustive block-seeding with a calibrated acceptance threshold. We then extend the guarantee to environments arriving sequentially, yielding a confidence guarantee that stays valid at every arrival, which one-shot exhaustive search cannot offer without repeating its full combinatorial search. We close by formalizing the intervention of a wise teacher who lifts a saturated learner off a plateau of boredom.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07057",
  "author_total": 1,
  "authors": [
    {
      "name": "Ernest Fokoué"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh0dfk907rmt2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07057",
  "fulltext_url": null,
  "id": "bh0dfk907rmt2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07057",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7220961846",
  "pdf_url": "https://arxiv.org/pdf/2610.07057",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh0dfk907rmt2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:32Z",
      "native_id": "2610.07057",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07057"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "sHAIL-Causal: A Sequential Staircase Procedure for Invariant Causal Predictor Discovery",
  "title_text": "sHAIL-Causal: A Sequential Staircase Procedure for Invariant Causal Predictor Discovery",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/bh0dfk907rmt2",
  "venue": "arXiv",
  "versions": []
}